Applying the definition of a perpendicular bisector, the value of k is: 4.
<h3>What is a Perpendicular Bisector?</h3>
A perfect example of a perpendicular bisector is segment XZ in the given diagram, which bisects another segment, WY at point X at right angles (angle 90 degrees), to form two equal segments, WX and XY. Therefore, a perpendicular bisector is a line that divides another line at right angles to form two equal segments.
We know the following:
XZ as a perpendicular bisector bisects segment WY into two halves, WX = XY.
WX = (6k + 8)
XY = (11k - 12)
To find k, plug in the values into the equation, WX = XY and solve for k:
6k + 8 = 11k - 12
Subtract 8 from both sides
6k + 8 - 8 = 11k - 12 - 8 [subtraction property of equality]
6k = 11k - 20
Subtract 11k from both sides
6k - 11k = 11k - 20 - 11k [subtraction property of equality]
-5k = -20
Divide both sides by -5
-5k/-5 = -20/-5 [subtraction property of equality]
k = 4
Therefore, applying the definition of a perpendicular bisector, the value of k is: 4.
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